##### 4.5.28 $$(x+1) y'(x)+(x+1)^4 y(x)^3+y(x)=0$$

ODE
$(x+1) y'(x)+(x+1)^4 y(x)^3+y(x)=0$ ODE Classiﬁcation

[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.267654 (sec), leaf count = 49

$\left \{\left \{y(x)\to -\frac {1}{\sqrt {(x+1)^2 \left (x^2+2 x+c_1\right )}}\right \},\left \{y(x)\to \frac {1}{\sqrt {(x+1)^2 \left (x^2+2 x+c_1\right )}}\right \}\right \}$

Maple
cpu = 0.017 (sec), leaf count = 40

$\left [y \left (x \right ) = \frac {1}{\sqrt {x^{2}+\textit {\_C1} +2 x}\, \left (1+x \right )}, y \left (x \right ) = -\frac {1}{\sqrt {x^{2}+\textit {\_C1} +2 x}\, \left (1+x \right )}\right ]$ Mathematica raw input

DSolve[y[x] + (1 + x)^4*y[x]^3 + (1 + x)*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> -(1/Sqrt[(1 + x)^2*(2*x + x^2 + C[1])])}, {y[x] -> 1/Sqrt[(1 + x)^2*(2
*x + x^2 + C[1])]}}

Maple raw input

dsolve((1+x)*diff(y(x),x)+y(x)+(1+x)^4*y(x)^3 = 0, y(x))

Maple raw output

[y(x) = 1/(x^2+_C1+2*x)^(1/2)/(1+x), y(x) = -1/(x^2+_C1+2*x)^(1/2)/(1+x)]